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Phrase(s): (I) wouldn’t bet on it. [and] (I) wouldn’t count on it.
Fig. I do not believe that something will happen. (Also with that or some specific happening. See examples.) • John: I’ll be a vice president in a year or two. Mary: I wouldn’t bet on that. • John: I’ll pick up a turkey on the day before Thanksgiving. Mary: Did you order one ahead of time? John: No. Mary: Then I wouldn’t count on it.
McGrawhill's American Idioms And Phrasal Verbs